Solute transport in porous media with solid‐liquid mass transfer limitations: Application to ion exchange

Abstract

Assuming that exchange equilibrium can be described by mass action laws, we show how to properly model the kinetic process with external and internal diffusion limitations using average concentrations and characteristic diffusion times. These characteristic diffusion times are defined as those used to describe linear interactions whereas the overall process is nonlinear due to the equilibrium constraints. The characteristic times are expressed in terms of the diffusion coefficients, characteristic dimensions of the exchanging aggregates, and relevant parameters of the flow regime. These expressions allow one to extrapolate laboratory measurements to field scale systems. The internal diffusion time is shown to be related to the selectivity factor. The analysis shows that external diffusion prevails in most situations, and specially at trace levels. A new criterion incorporating the nonlinear equilibrium law is proposed to determine whether the rate‐limiting step is internal or external diffusion.